The simple interest on a certain sum of money at the rate of 5% p.a. for four years is Rs. 420. At what rate of interest, the same amount of interest can be received on the same sum after two and half years?
8%
To solve this problem, we need to determine the rate of interest that would yield the same amount of simple interest (Rs. 420) on the same principal over a period of 2.5 years. Let's break down the steps:
- Understand Simple Interest Formula:
The formula for simple interest is given by:
\(SI = \frac{P \times R \times T}{100}\)
where \(SI\) is the simple interest, \(P\) is the principal amount, \(R\) is the rate of interest per annum, and \(T\) is the time in years.
- Calculate the Principal:
We know that the simple interest for 4 years at 5% per annum is Rs. 420. Using the formula, we have:
\(420 = \frac{P \times 5 \times 4}{100}\)
Simplifying this, we get:
\(420 = \frac{20P}{100}\)
\(420 \times 5 = P\)
\(P = 2100\)
- Determine the Required Rate for 2.5 Years:
Given the principal \(P = 2100\), interest \(SI = 420\), and time \(T = 2.5\) years, we need to find the rate \(R\) that satisfies the condition:
\(420 = \frac{2100 \times R \times 2.5}{100}\)
Simplifying this, we get:
\(420 = \frac{5250R}{100}\)
\(420 \times 100 = 5250R\)
\(R = \frac{42000}{5250}\)
\(R = 8\%\)
Conclusion: The rate of interest required for the same simple interest over 2.5 years is 8%. Thus, the correct option is 8%.
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